Added June 2, 2019.
Problem 3.3(d) nonlinear pde’s by Lokenath Debnath, 3rd edition.
Solve for \(u(x,y)\) \[ (1+x^2) u_x+ u_y=0 \]
Mathematica ✓
ClearAll["Global`*"]; pde = (1+x^2)*D[u[x, y], x] + D[u[x, y], y] ==0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde ,u[x, y], {x, y}], 60*10]];
\[\left \{\left \{u(x,y)\to c_1\left (y-\tan ^{-1}(x)\right )\right \}\right \}\]
Maple ✓
restart; pde :=(1+x^2)*diff(u(x,y),x)+diff(u(x,y),y)=0; cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,u(x,y))),output='realtime'));
\[u \left (x , y\right ) = \textit {\_F1} \left (y -\arctan \left (x \right )\right )\]
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